Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}2x+6y &= -4 \\ 3x-6y &= 6\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-6y = -3x+6$ Divide both sides by $-6$ to isolate $y$ $y = {\dfrac{1}{2}x - 1}$ Substitute this expression for $y$ in the first equation. $2x+6({\dfrac{1}{2}x - 1}) = -4$ $2x + 3x - 6 = -4$ Simplify by combining terms, then solve for $x$ $5x - 6 = -4$ $5x = 2$ $x = \dfrac{2}{5}$ Substitute $\dfrac{2}{5}$ for $x$ back into the top equation. $2( \dfrac{2}{5})+6y = -4$ $\dfrac{4}{5}+6y = -4$ $6y = -\dfrac{24}{5}$ $y = -\dfrac{4}{5}$ The solution is $\enspace x = \dfrac{2}{5}, \enspace y = -\dfrac{4}{5}$.